<h2>Problem 226</h2>
<div style="color:#666;font-size:80%;">02 January 2009</div><br />
<div class="problem_content">
<p>The <i>blancmange curve</i> is the set of points (<var>x</var>,<var>y</var>) such that 0&thinsp;<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />&thinsp;<var>x</var>&thinsp;<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />&thinsp;1 and <img src="project/images/p_226_formula.gif" style="vertical-align:middle;" alt="" /> ,<br />where <var>s</var>(<var>x</var>) = the distance from <var>x</var> to the nearest integer.</p>

<p>The area under the blancmange curve is equal to &frac12;, shown in pink in the diagram below.</p>

<div style="text-align:center;">
<img src="project/images/p_226_scoop2.gif" alt="blancmange curve" /></div>

<p>Let <var>C</var> be the circle with centre (&frac14;,&frac12) and radius &frac14;, shown in black in the diagram.</p>

<p>What area under the blancmange curve is enclosed by <var>C</var>?<br />Give your answer rounded to eight decimal places in the form <i>0.abcdefgh</i></p>

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